We sequenced the genome of the highly heterozygous almond Prunus dulcis cv. Texas combining short- and long-read sequencing. We obtained a genome assembly totaling 227.6 Mb of the estimated almond genome size of 238 Mb, of which 91% is anchored to eight pseudomolecules corresponding to its haploid chromosome complement, and annotated 27 969 protein-coding genes and 6747 non-coding transcripts. By phylogenomic comparison with the genomes of 16 additional close and distant species we estimated that almond and peach (Prunus persica) diverged around 5.88 million years ago. These two genomes are highly syntenic and show a high degree of sequence conservation (20 nucleotide substitutions per kb). However, they also exhibit a high number of presence/absence variants, many attributable to the movement of transposable elements (TEs). Transposable elements have generated an important number of presence/absence variants between almond and peach, and we show that the recent history of TE movement seems markedly different between them. Transposable elements may also be at the origin of important phenotypic differences between both species, and in particular for the sweet kernel phenotype, a key agronomic and domestication character for almond. Here we show that in sweet almond cultivars, highly methylated TE insertions surround a gene involved in the biosynthesis of amygdalin, whose reduced expression has been correlated with the sweet almond phenotype. Altogether, our results suggest a key role of TEs in the recent history and diversification of almond and its close relative peach.